1. Field of Invention The field of invention relates to vibration control devices of the active type for reducing the response of a structure to earthquake and wind vibrations or the like, by applying a control force on the structure. These devices are suitable for vibration control of large scale structures having comparatively long natural periods, such as multi-storied buildings and high rises.
2. Description of Related Art
As used in this specification, symbols and terms are defined as follows:
c.sub.d --coefficient of damping PA1 h.sub.d --damping factor PA1 k.sub.b, k.sub.d, and k.sub.1 --spring coefficients of stiffness PA1 m.sub.1 --mass of building structure PA1 m.sub.a --first additional mass PA1 m.sub.b --second additional mass PA1 u(t)--actuator control force PA1 x.sub.a --displacement of first additional mass PA1 x.sub.b --displacement of second additional mass PA1 x.sub.1 --displacement of building structure PA1 Active mass damper (AMD)--a mass damper energized solely by a man-made control force such as hydraulic, electromagnetic, electrical, electro-mechanical means, or any combination thereof. PA1 Passive mass damper (DD)--a mass damper energized solely from the energy of seismic (or wind) vibration. PA1 G.sub.1, G.sub.2 or G.sub.3 is a predetermined gain in each term of the above equation (1), PA1 (d.sup.2 x.sub.1 /dt.sup.2) is a response acceleration of the structure, PA1 (dx.sub.b /dt) is a speed of the first additional mass body, and PA1 (x.sub.b -x.sub.a) is a relative displacement of the first additional mass body to the driver. PA1 G.sub.1, G.sub.2, G.sub.3, or G.sub.4 is a predetermined gain in each term of the above equation (3), PA1 (dx.sub.1 /dt) is a response speed of the structure, PA1 (x.sub.a -x.sub.1) is a relative displacement of the first additional mass body to the structure, PA1 (dx.sub.b /dt) is a speed of the first additional mass body, and PA1 (x.sub.b -x.sub.a) is a relative displacement of the first additional mass body to the driver.
Dynamic dampers (designated hereinafter as DD) of the passive type are disclosed in Japanese Pat. Laid-open No. 63-76932 and Japanese Pat. Publication No. 3-38386.
Prior art FIG. 6 of this application shows a vibration model of a DD to be applied to a structure, wherein m.sub.1 is a mass of a main body of a structure constituting a main vibration system, and m.sub.d is a mass of an additional mass body constituting a damping system. Also, k.sub.1 is a spring constant of the main body of the structure. The main body of the structure having a mass m.sub.1 and the additional mass body are mutually connected through a spring having a spring constant k.sub.d and a damper having a damping coefficient c.sub.d. Further, x.sub.1 represents a displacement of the structure, and x.sub.d represents a displacement of the additional mass body m.sub.d.
A natural angular frequency of the main vibration system is given by: EQU .omega..sub.1 =(k.sub.1 /m.sub.1).sup.1/2
In the DD, a mass m.sub.d of the damping system is designed so that the ratio of the mass m.sub.d to the mass.sub.1 of the main vibration system may be set to be or equal to: EQU .mu.=m.sub.d /m.sub.1 .gtoreq.0.01.
At this time, the natural angular frequency of the damping system is given by: EQU .omega..sub.d =(1/1+.mu.).omega..sub.1
A damping coefficient c.sub.d and a damping factor h.sub.d are respectively represented by: EQU c.sub.d =2m.sub.d .omega..sub.d h.sub.d EQU h.sub.d =[3.mu./8(1+.mu.)].sup.1/2
Active type control devices, or Active Mass Drivers (designated hereinafter as AMD) are disclosed in U.S. Pat. No. 5,022,201.
Prior art FIG. 7 of this application shows a vibration model of an AMD which applies a control force u(t) by an actuator such as a hydraulic or electromagnetic device, between a main body of the structure having a mass m.sub.1 and an additional mass body having a mass m.sub.d to actively control the vibration of the structure.
In the AMD, assuming that a spring between the main body of the structure and the additional mass body constituting a vibration control device is set under a soft condition, i.e., EQU .omega..sub.d .ltoreq.(1/2).omega..sub.1
the control force u(t) is given in the following equation: EQU u(t)=G.sub.1 (dx.sub.1 /d.sub.t)+G.sub.2 (dx.sub.d /dt)
wherein G.sub.1 is a gain in a circuit including an automatic gain control circuit (AGC) or the like against the response speed of the structure and attains the correspondences of large inputs through small inputs. The second term in the above equation gives a damping property to the side of the additional mass body as well to attain stability thereof by adding the product of a gain G.sub.2 (negative sign) to a vibration speed on the side of the additional mass body to the control force.
In response to the above defined AMD, some studies have been made which add a spring having a spring constant k.sub.d in parallel with the control force due to the actuator as shown in the vibration model of FIG. 8 and to obtain a vibration control effect to the same degree with that of the AMD by means of less control force in comparison with that of the AMD (designated hereinafter as ATMD, the abbreviation for Active Tuned Damper.)
In an ATMD, a spring constant k.sub.d is set so that the vibration of an additional mass body may synchronize with that of a structure, that is, EQU .omega..sub.d =.omega..sub.1
and the resulting control force u(t) is, for example, given by the following equation: EQU u(t)=G.sub.1 (dx.sub.1 /dt)+G.sub.2 (dx.sub.d /dt)+G.sub.3 (x.sub.1 -x.sub.d)
wherein G.sub.3 is a gain having a negative sign and cancels a part of the inertial force applying on the additional mass body at a vibration time due to the third term in the above equation so that the additional mass body may be vibrated by less control force.
Japanese Pat. Publication No. 3-70075 discloses means for controlling the structural vibration due to earthquake or the like by an extremely small control force by connecting a second additional mass body having a mass less than that of the additional mass body of a DD to the additional mass body of the DD through a spring and an actuator and applying a control force to the second additional mass body from the actuator, as it were, an active type vibration control device in a form of a double dynamic damper.
The conventional vibration control device as described above has an advantage in that the DD needs no energy supply to the device, but the vibration control effect is determined by the mass ratio of the structure to the additional mass body. Therefore, the DD needs the additional mass body with a large mass before any significant vibration control can be expected.
The AMD gets a large control effect by using an additional mass body with less mass in comparison with that of the DD. However, since an energy supply is necessary, the design of a control force circuit, provision for security and stability of the device, and the prevention of malfunction are necessary.
As described above, the ATMD has an advantage in that the control force can be lessened in comparison with that of the AMD, but the ATMD has similar disadvantages to those of the AMD. The ATMD can easily produce noise and vibration problems since the device for applying the control force directly produces a reaction force to the structure.
The present invention presents a novel solution for the problems in the above-described conventional vibration control devices.